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Simplifying ln(8) = ln(x + 4) + -1ln(16) Reorder the terms for easier multiplication: 8ln = ln(x + 4) + -1ln(16) Reorder the terms: 8ln = ln(4 + x) + -1ln(16) 8ln = (4 * ln + x * ln) + -1ln(16) 8ln = (4ln + lnx) + -1ln(16) Reorder the terms for easier multiplication: 8ln = 4ln + lnx + -1 * 16ln Multiply -1 * 16 8ln = 4ln + lnx + -16ln Reorder the terms: 8ln = 4ln + -16ln + lnx Combine like terms: 4ln + -16ln = -12ln 8ln = -12ln + lnx Solving 8ln = -12ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '12ln' to each side of the equation. 8ln + 12ln = -12ln + 12ln + lnx Combine like terms: 8ln + 12ln = 20ln 20ln = -12ln + 12ln + lnx Combine like terms: -12ln + 12ln = 0 20ln = 0 + lnx 20ln = lnx Add '-1lnx' to each side of the equation. 20ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 20ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(20 + -1x) = 0Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve: Simplifying 20 + -1x = 0 Solving 20 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1x = 0 + -20 -1x = 0 + -20 Combine like terms: 0 + -20 = -20 -1x = -20 Add 'x' to each side of the equation. -1x + x = -20 + x Combine like terms: -1x + x = 0 0 = -20 + x Simplifying 0 = -20 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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